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Homework 01 Solutions

# Homework 01 Solutions - homework 01 GADHIA TEJAS Due 4:00...

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homework 01 – GADHIA, TEJAS – Due: Jan 27 2007, 4:00 am 1 Question 1 part 1 of 1 10 points A spherical balloon with radius r inches has volume 4 3 πr 3 . Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 2 inches. 1. 4 3 πr 3 2. 4 3 π ( 4 r + 6 r 2 + 8 ) 3. 4 3 π ( r + 2) 3 4. 4 3 π ( 12 r + 2 r 2 + 8 ) 5. 4 3 π ( 12 r + 6 r 2 + 8 ) correct Explanation: Question 2 part 1 of 1 10 points An open rectangular box with volume 2 m 3 has a square base. Express the surface area of the box as a function S ( x ) of the length x of a side of the base. 1. S ( x ) = 2 x + 2 x 2. S ( x ) = x 2 + 4 x 2 3. S ( x ) = x 2 + 8 x correct 4. S ( x ) = x 2 + 4 x 5. S ( x ) = 2 x 2 + 2 x 2 6. S ( x ) = x 2 + 8 x 2 Explanation: Question 3 part 1 of 1 10 points A newly discovered Jupiter-like planet has an average radius 11 times that of the Earth and a mass 314 times that of the Earth. Calculate the ratio of new planet’s mass density to the mass density of the Earth. Correct answer: 0 . 235913 (tolerance ± 1 %). Explanation: Let : R np = 11 R E and M np = 314 M E . The volume of a sphere of radius R is V = 4 3 π R 3 . The (average) density ρ of a body is the ratio of the body’s mass to its volume, ρ = M/V . Planets are spherical, so the (average) density of a planet of a given mass M and a given radius R is ρ = M 4 3 π R 3 . Comparing the newly discovered planet to the Earth, we have ρ np ρ E = parenleftBigg M np 4 3 π R 3 np parenrightBigg slashbigg parenleftBigg M E 4 3 π R 3 E parenrightBigg = parenleftbigg M np M E parenrightbiggslashbiggparenleftbigg R np R E parenrightbigg 3 = 314 (11) 3 = 0 . 235913 . Question 4 part 1 of 1 10 points The number x = 0 . 0416 has how many significant digits? Correct answer: 3 (tolerance ± 1 %). Explanation: Figures except zeros to the left of the first nonzero digit are all of significance.

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homework 01 – GADHIA, TEJAS – Due: Jan 27 2007, 4:00 am 2 Question 5 part 1 of 2 10 points A person travels by car from one city to another. She drives for 21 . 1 min at 81 . 8 km / h, 14 . 1 min at 86 . 4 km / h, 49 min at 36 km / h, and spends 13 . 5 min along the way eating lunch and buying gas. Determine the distance between the cities along this route. Correct answer: 78 . 4703 km (tolerance ± 1 %). Explanation: Distances traveled are x 1 = v 1 t 1 x 2 = v 2 t 2 x 3 = v 3 t 3 Then the total distance traveled is x = x 1 + x 2 + x 3 = (28 . 7663 km) + (20 . 304 km) + (29 . 4 km) = 78 . 4703 km .
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Homework 01 Solutions - homework 01 GADHIA TEJAS Due 4:00...

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